Finite Group Databasebeta

← #14654643

Subgroups — #14654643

Order 2816.

528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078655C212yesmaximal
2#13069597C211yesmaximal, characteristic
3#13067045C212yesmaximal
4#13066445C211yesmaximal, characteristic
5C11×#2399C211yesmaximal, characteristic
6C2×C4×Q8×C11C2212yes—
7#10623001C2211yescharacteristic
8C11×#398—22no—
9C11×#395—22no—
10C4×C11×C4⋊C4—22no—
11C11×#376C2211yescharacteristic
12#10622841—22no—
13#10622644—22no—
14C4×#4326—24no—
15#10622634—22no—
16#10622583—22no—
17#10622538C2212yes—
18#10622537C2211yescharacteristic
19Q8⋊(C11⋊C8)—24no—
20#10622161—22no—
21C22×Q8×C11D412yes—
22C4×Q8×C11—22no—
23C4×Q8×C11—22no—
24C4×Q8×C11—22no—
25C4×Q8×C11—22no—
26C2×C11×C4⋊C4—24no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4D412yes—
29C2×C42×C11—22no—
30C2×C42×C11D412yes—
31C2×C42×C11C2311yescharacteristic
32C2×#4326—24no—
33#66979—21no—
34#66977—22no—
35C2×#4318—21no—
36#66923—21no—
37#66922D412yes—
38C4×Dic22—22no—
39C11×#95—22no—
40C11×#95—22no—
41C11×#95—22no—
42#66899—24no—
43C22⋊(C11⋊C8)—22no—
44#66874—24no—
45#66871—24no—
46C4⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—22no—
48C4×C11⋊C8D414yes—
49#10017—111nomaximal, Sylow
50C2×Q8×C11—22no—
51C2×Q8×C11—22no—
52C2×Q8×C11—44no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11C2×D412yes—
57C22×C4×C11C2×D411yescharacteristic
58C2×Dic22—22no—
59C11×C4⋊C4—22no—
60C11×C4⋊C4—22no—
61C11×C4⋊C4—48no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—42no—
64C42×C11—22no—
65C42×C11—42no—
66C42×C11—42no—
67C42×C11Q1614yescomplemented
68C42×C11C2×D411yescharacteristic
69C42×C11C2×D412yes—
70C42×C11#4111yescharacteristic
71C22⋊Dic11—41no—
72#4326—48no—
73C4⋊Dic11—22no—
74C4⋊Dic11—22no—
75Dic11⋊C4—42no—
76C4×Dic11—41no—
77#4318—42no—
78C2×C11⋊C8—24no—
79C2×C11⋊C8—41no—
80#3104—112no—
81#2399D1111yescharacteristic
82#1995—111no—
83#1487—112no—
84#1274—111no—
85C23×C11#12011yescharacteristic
86Q8×C11—24no—
87Q8×C11—24no—
88Q8×C11—42no—
89Q8×C11—42no—
90C2×C4×C11—24no—
91C2×C4×C11—24no—
92C2×C4×C11—42no—
93C2×C4×C11—44no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—44no—
97C2×C4×C11—42no—
98C2×C4×C11#12012yes—
99C2×C4×C11#12111yescharacteristic
100C2×C4×C11#12112yes—
101C2×C4×C11#12711yescharacteristic
102C2×C4×C11C2×Q1612yes—
103C2×C4×C11#13712yes—
104C2×Dic11—42no—
105Dic22—44no—
106C11⋊C8—44no—
107C11⋊C8—81no—
108#533—111no—
109C2×C4×Q8C2×D1112yes—
110#484—222no—
111#477—222no—
112#462—222no—
113#451—222no—
114C4×Q16—224no—
115#431—112no—
116#423—111no—
117#398—22no—
118#395—22no—
119C4×C4⋊C4—22no—
120#376C2×D1111yescharacteristic
121#339—222no—
122Q8⋊C8—224no—
123C22×C11—22no—
124C22×C11#39211yescharacteristic
125C22×C11#45112yes—
126C4×C11—22no—
127C4×C11—22no—
128C4×C11—44no—
129C4×C11—44no—
130C4×C11—82no—
131C4×C11#46212yes—
132C4×C11#49411yescharacteristic
133C4×C11#49711yescharacteristic
134Dic11—82no—
135C22×Q8C22⋊D1112yes—
136C2×Q16—224no—
137C2×M16—221no—
138C4⋊Q8—112no—
139#125—221no—
140C22⋊Q8—222no—
141C4×Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—222no—
146#117—221no—
147C2×C4⋊C4—24no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4C22⋊D1112yes—
150C2×C42—22no—
151C2×C42C22⋊D1112yes—
152C2×C42C22×D1111yescharacteristic
153#107—224no—
154C4⋊C8—222no—
155C4⋊C8—222no—
156#103—224no—
157#103—224no—
158C22⋊C8—222no—
159C4×C8—114no—
160#95—22no—
161#95—22no—
162#95—22no—
163C2×C11—22no—
164C2×C11#201012yes—
165C2×C11#201611yescharacteristic
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—44no—
169C2×Q8—222no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4C2×C22⋊D1112yes—
174C22×C4C2×C22⋊D1111yescharacteristic
175Q16—448no—
176M16—442no—
177C2×C8—224no—
178C2×C8—441no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—48no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—222no—
185C4⋊C4—222no—
186C4⋊C4—442no—
187C22⋊C4—441no—
188C42—22no—
189C42—42no—
190C42—42no—
191C42—441no—
192C42#432614yescomplemented
193C42D4×D1111yescharacteristic
194C42D4×D1112yes—
195C42#434111yescharacteristic
196C11#1001711yescharacteristic, complemented, Sylow
197C23#6700611yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—42no—
201Q8—42no—
202Q8—444no—
203C2×C4—24no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—44no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—44no—
210C2×C4—42no—
211C2×C4—442no—
212C2×C4#6699012yes—
213C2×C4#6699111yescharacteristic
214C2×C4#6699212yes—
215C2×C4#6699311yescharacteristic
216C2×C4#6699512yes—
217C2×C4C2×#432612yes—
218C8—444no—
219C8—881no—
220C22—22no—
221C22#1062283611yescharacteristic
222C22#1062284112yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—44no—
227C4—82no—
228C4—882no—
229C4#1062269911yescharacteristic
230C4#1062270312yes—
231C4#1062270511yescharacteristic
232C2—22no—
233C2#1306968112yes—
234C2#1306971611yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2399C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#2399D11
hypocenterC11#10017
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2399

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
67. C42×C11Q16semidirect
192. C42#4326semidirect
196. C11#10017semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130786552
#130695972
#130670452
#130664452
C11×#23992
#1001711